Comptes Rendus
no. 12
Algebra/Homological algebra
Some properties of the extremal algebras
[Quelques propriétés des algèbres extrémales]

Présenté par : the Editorial Board

Shengqiang Wang1 ; Quanshui Wu2
1 Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
2 School of Mathematical Sciences, Fudan University, Shanghai 200433, China
Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 985-990.

En nous appuyant sur les travaux de Fløystad et Vatne, nous décrivons quelques propriétés homologiques des algèbres extrémales. Plus précisément, nous montrons que les algèbres extrémales sont intègres, nœthériennes, régulières au sens d'Auslander, de Cohen–Macaulay et de Calabi–Yau. Nous calculons également les modules cycliques de la série de Hilbert (1−t)−1 sur ces algèbres extrémales.

The (generalized) extremal algebra [4] is Noetherian, Auslander regular and Cohen–Macaulay. A necessary and sufficient condition is given for the generalized extremal algebras being Calabi–Yau. The point modules over these algebras are described explicitly.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.09.028
Shengqiang Wang 1 ; Quanshui Wu 2

1 Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
2 School of Mathematical Sciences, Fudan University, Shanghai 200433, China 
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Shengqiang Wang; Quanshui Wu. Some properties of the extremal algebras. Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 985-990. doi : 10.1016/j.crma.2014.09.028. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.028/

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[4] G. Fløystad; J.E. Vatne Artin–Schelter regular algebras of dimension five, Algebras, Geometry and Mathematical Physics, Banach Center Publ., vol. 93, 2011, pp. 19-39

[5] N. Jing; J.J. Zhang Gorensteinness of invariant subrings of quantum algebras, J. Algebra, Volume 221 (1999), pp. 669-691

[6] P. Jorgensen; J.J. Zhang Gourmet's guide for Gorensteinness, Adv. Math., Volume 151 (2000), pp. 313-345

[7] M. Reyes; D. Rogalski; J.J. Zhang Skew Calabi–Yau algebras and homological identities, Adv. Math., Volume 264 (2014), pp. 308-354

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[11] G.-S. Zhou; D.-M. Lu Artin–Schelter regular algebras of dimension five with two generators, J. Pure Appl. Algebra, Volume 218 (2014), pp. 937-961

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